Properties

Label 2790.k
Number of curves $4$
Conductor $2790$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("k1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2790.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2790.k1 2790l4 \([1, -1, 0, -5719239, 5265909873]\) \(28379906689597370652529/1357352437500\) \(989509926937500\) \([6]\) \(69120\) \(2.3546\)  
2790.k2 2790l3 \([1, -1, 0, -356859, 82633365]\) \(-6894246873502147249/47925198774000\) \(-34937469906246000\) \([6]\) \(34560\) \(2.0081\)  
2790.k3 2790l2 \([1, -1, 0, -76779, 5903685]\) \(68663623745397169/19216056254400\) \(14008505009457600\) \([2]\) \(23040\) \(1.8053\)  
2790.k4 2790l1 \([1, -1, 0, 12501, 600453]\) \(296354077829711/387386634240\) \(-282404856360960\) \([2]\) \(11520\) \(1.4587\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 2790.k have rank \(0\).

Complex multiplication

The elliptic curves in class 2790.k do not have complex multiplication.

Modular form 2790.2.a.k

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + q^{5} + 2 q^{7} - q^{8} - q^{10} - 4 q^{13} - 2 q^{14} + q^{16} - 6 q^{17} + 8 q^{19} + O(q^{20})\)  Toggle raw display

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.